Police official Abdul Jalil, quoting witnesses, said the attackers fled the scene after killing 50-year-old Nikhil Chandra Joardar outside his shop in the town of Tangail, 80 km (50 miles) northwest of the capital Dhaka.
Islamic State militants claimed responsibility for the killing, saying the tailor had blasphemed Prophet Mohammad, the U.S.-based monitoring service SITE said.
The attack came days after a Bangladeshi gay rights campaigner and his friend were killed in a similar manner in a Dhaka apartment.
The Muslim-majority nation of 160 million people has seen a surge in violent attacks over the past few months in which liberal activists, members of minority Muslim sects and other religious groups have been targeted.
Police said they were investigating whether Joardar's killing was connected to a complaint made against him for making a derogatory comment about Prophet Mohammad.
He was jailed for a few weeks in 2012 but released after the complaint against him was withdrawn, said Jalil.
The Islamic State and a group affiliated to al Qaeda have issued similar claims of responsibility in the past, but the authenticity of Saturday's statement could not be immediately verified.
The Bangladeshi government has denied that Islamic State or al Qaeda have a presence in the country. Police say home-grown militants groups are behind the attacks.
Western security experts doubt that there are any direct operational links between Islamic State, based in the Middle East, and militants operating on the ground in Bangladesh.
But they do say that a "call and response" of claims and statements of support for militant attacks through their propaganda channels allows them to create the impression of being in league together.
Human rights activists have urged mainstream politicians in Bangladesh to abandon sectarian hostilities that date back to the 1971 war of independence, and to engage in a constructive dialogue that would deprive Islamist extremists of cover for their attacks.
